GCF & LCM Calculator
Find the Greatest Common Factor and Least Common Multiple of any two numbers, with step-by-step working.
GCF vs LCM — Key Differences
| GCF | LCM | |
|---|---|---|
| Full name | Greatest Common Factor | Least Common Multiple |
| Also called | GCD, HCF | LCM |
| Result is always… | ≤ smaller number | ≥ larger number |
| Main use | Simplify fractions | Find common denominators |
| Example (12, 18) | GCF = 6 | LCM = 36 |
Frequently Asked Questions
What is the Greatest Common Factor (GCF)?
The Greatest Common Factor (also called the Greatest Common Divisor or GCD) is the largest positive integer that divides evenly into two or more numbers with no remainder. For example, the GCF of 48 and 18 is 6, because 6 is the largest number that divides both 48 (48 ÷ 6 = 8) and 18 (18 ÷ 6 = 3).
What is the Least Common Multiple (LCM)?
The Least Common Multiple is the smallest positive integer that is divisible by both numbers. For example, the LCM of 4 and 6 is 12 — the smallest number that both 4 and 6 divide into evenly. LCM is used when adding fractions with different denominators (you need to find a common denominator).
What is the Euclidean algorithm?
The Euclidean algorithm is an efficient method for finding the GCF. It works by repeatedly dividing the larger number by the smaller and replacing the larger with the remainder, until the remainder is 0. The last non-zero remainder is the GCF. For 48 and 18: 48 = 2×18 + 12, then 18 = 1×12 + 6, then 12 = 2×6 + 0. GCF = 6.
What is the relationship between GCF and LCM?
There is a simple formula connecting them: GCF(a, b) × LCM(a, b) = a × b. This means once you know the GCF, you can find the LCM with: LCM = (a × b) / GCF. For 48 and 18: GCF = 6, LCM = (48 × 18) / 6 = 864 / 6 = 144.
How are GCF and LCM used in real life?
GCF is used for simplifying fractions (divide numerator and denominator by their GCF). LCM is used for finding common denominators when adding or subtracting fractions. In scheduling, LCM finds when two recurring events will coincide — for example, if event A repeats every 4 days and event B every 6 days, they next coincide in LCM(4,6) = 12 days.